The differential operator $L = D^2 + D + cI$ acts on span$\{1, x, x^2, x^3\} \subset \mathbb{C}[x]$.
(a) Find the matrix of $L$ with respect to the basis $X = \{1, x, x^2, x^3\}$ and
determine $\sigma(L)$.
(b) Find the Jordan form of $L$.
(c) Find a $\mathbb{C}$-basis that puts $[L]_X$ into Jordan form.